Instructions:Read the assertion and reason carefully to mask...

Instructions:Read the assertion and reason carefully to mask the correct option out of the options given below. (A) If both assertion and reason are true and the reason is the correct explanation of the assertion. (B) If both assertion and reason are true but reason is not be correct explanation of assertion. (C) If assertion is true but reason is false. (D) If the assertion and reason both are false. Assertion: The total translation kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its Pressure and its volume. Reason: The molecules of a gas collide with each other and velocities of the molecules change due to the collision (A) D (B) $\mathrm{C}$ (C) A (D) B

Instructions:Read the assertion and reason carefully to mask the correct option out of the options given below.
(A) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(B) If both assertion and reason are true but reason is not be correct explanation of assertion.
(C) If assertion is true but reason is false.
(D) If the assertion and reason both are false.
Assertion: The total translation kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its Pressure and its volume. Reason: The molecules of a gas collide with each other and velocities of the molecules change due to the collision
(A) D
(B) $\mathrm{C}$
(C) A
(D) B

Key Concepts

Ideal Gas Law

The Ideal Gas Law establishes the relationship between pressure, volume, temperature, and the number of moles of a gas. It is generally expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature. This law is fundamental in understanding the behavior of gases under various conditions and serves as the backbone for many concepts in thermodynamics and kinetic theory.

Kinetic Theory of Gases

The Kinetic Theory of Gases provides a molecular-level explanation of the properties of gases, linking microscopic motions of molecules to macroscopic observables like pressure and temperature. It explains that gas pressure arises due to collisions of rapidly moving particles with the walls of a container, and that the kinetic energy of the molecules is directly proportional to the absolute temperature. This theory forms the basis for deriving expressions related to the internal energy and work performed by gases.

Translational Kinetic Energy

Translational kinetic energy refers to the energy associated with the random motion of particles moving in space. In the context of an ideal gas, the total translational kinetic energy of the gas molecules is proportional to the temperature of the gas, typically given by the expression (3/2) nRT. This concept is crucial because it connects the microscopic motion of particles with the macroscopic thermal properties of the gas.

Molecular Collisions

Molecular collisions describe the random interactions between gas molecules which are fundamental to the kinetic theory. These collisions are responsible for the distribution of velocity and energy among the molecules, and they play a key role in establishing equilibrium states such as temperature distribution. However, while collisions are essential for understanding pressure and energy distribution, they do not necessarily serve as a direct explanation for specific thermodynamic relationships like the proportionality between total kinetic energy and the product of pressure and volume.

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